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The moment of inertia of a body about a given axis is 1.2 kg m². Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration of 25 radian/sec² must be applied about that axis for a duration of

1. 4 seconds
2. 2 seconds
3. 8 seconds
4. 10 seconds

Correct answer: 2 seconds

Solution

The rotational kinetic energy is given by \( KE = \frac{1}{2} I \omega^2 \). Substituting \( KE = 1500 \) J and \( I = 1.2 \) kg·m², we find \( \omega = 50 \) rad/s. Using \( \omega = \alpha t \) with \( \alpha = 25 \) rad/s², we solve for \( t = \frac{\omega}{\alpha} = \frac{50}{25} = 2 \) seconds.

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